1. Field of the Invention
This invention relates generally to thermoelectric materials and more particularly to quantum dot superlattice structures.
2. Description of the Related Art
As is known in the art, there exists a class of materials referred to as thermoelectric materials. A thermoelectric material is a type of material which can directly convert thermal energy into electrical energy or vice versa.
Although certain thermoelectric materials have been known in the art for a number of years (e.g.xe2x80x94bulk semiconductors), it has only recently been found that thermoelectric materials having a superlattice structure can possess thermoelectric properties which are better than the corresponding thermoelectric properties of other thermoelectric materials.
A superlattice structure denotes a composite structure made of alternating ultrathin layers of different component materials. A superlattice structure typically has an energy band structure which is different than, but related to, the energy band structures of its component materials. The selection of the component materials of a superlattice structure, and the addition of relative amounts of those component materials, will primarily determine resulting properties of a superlattice structure as well as whether, and by how much, those properties will differ from those of the superlattice structure""s component material antecedents.
It is generally known that thermoelectric materials and thermoelectric materials having a superlattice structure find application in the fields of power generation systems, and the heating and/or cooling of materials. One problem, however, is that although these fields place ever-increasing demands on thermoelectric materials to possess ever-improving thermoelectric performance characteristics, the thermoelectric materials and thermoelectric materials having a superlattice structure known in the art have, as of yet, not been able to keep pace with such performance demands.
One way to predict the thermoelectric behavior of thermoelectric materials or thermoelectric materials having a superlattice structure in the fields of power generations systems, and the heating and/or cooling of materials is to calculate a thermoelectric figure of merit for the materials. The thermoelectric figure of merit, ZT, is a dimensionless material parameter in which T corresponds to temperature and Z is the figure of merit. ZT is a measure of the utility of a given thermoelectric material or thermoelectric materials having a superlattice structure in power generation systems, and heating and/or cooling applications at a temperature T.
The relationship of ZT to the material properties of thermoelectric materials and thermoelectric materials having a superlattice structure is shown by the following equation:
ZT=S2"sgr"T/xcexa=S2 nexcexcT/(xcexa1+xcexae)=PF T/K=S2 GT/K
in which S, "sgr", T and xcexa are, respectively, the Seebeck coefficient, the electrical conductivity, the temperature, and the thermal conductivity and where n, e, xcexc, xcexa1 and xcexae are, respectively, the carrier density, the electronic charge, the carrier mobility, the lattice part of the thermal conductivity and the electronic part of the thermal conductivity, and where PF is the power factor, and where G and K are, respectively, the electrical conductance and the thermal conductance.
Generally, it is known in the art that it is desirable for thermoelectric materials to have a relatively high value for their thermoelectric figure of merit (ZT) in order for those thermoelectric materials to perform well in the fields of power generation systems and the heating and/or cooling of materials. From inspection of the above equation, it appears that to provide a thermoelectric material having a high ZT, one need only fabricate on it a superlattice structure having relatively high values for its Seebeck coefficient, its electrical conductivity, and its temperature while, at the same time, having a relatively low value for its thermal conductivity.
It has proven difficult in practice to provide a thermoelectric material or a thermoelectric material having a superlattice structure that has a high thermoelectric figure of merit (ZT) value. Past findings in the art have suggested that the inherent interrelationships between the material properties included in the above equation for ZT such as carrier mobility, lattice thermal conductivity, power factor and Seebeck coefficient may limit, or place a ceiling upon, the ZT values of thermoelectric materials or thermoelectric materials having a superlattice structure.
As is also known in the art, multilayer systems prepared by molecular beam epitaxy (MBE) can provide materials having improved thermoelectric properties. Superlattice systems having reduced dimensionality have been proposed as a means to greatly enhance the thermoelectric figure of merit (ZT) as a result of the effects of confinement on the electronic density of states. It has also been shown that additional effects need to be included in order to obtain a more complete understanding of these complex structures.
The above discoveries have led to increasing interest in quantum-well and quantum-wire superlattice structures in the search to find improved thermoelectric materials for applications in cooling and power generation. Investigation of Pb1xe2x88x92xEuxTe/PbTe quantum-well superlattices grown by MBE yielded an enhanced ZT due to the quantum confinement of electrons in the well part of the superlattice structure have been conducted.
Quantum wells have two-dimensional carrier confinement whereas quantum wires have one-dimensional confinement of the carrier. Quantum wires have been calculated to have much higher ZTs than quantum wells due to improved confinement. And, it has been recognized that quantum dots (QDs) may have even higher ZT values than quantum wires.
Quantum dots have zero-dimensional confinement and represent the ultimate in reduced dimensionality, i.e. zero dimensionality. The energy of an electron confined in a small volume by a potential barrier as in a QD is strongly quantized, i.e., the energy spectrum is discrete. For QDs, the conduction band offset and/or strain between the QD and the surrounding material act as the confining potential. The quantization of energy, or alternatively, the reduction of the dimensionality is directly reflected in the dependence of the density of states on energy. For a zero-dimensional system (e.g. a QD superlattice), the density of states (dN/dE) of the confined electrons has the shape of a delta-like function       dN    /    dE    ⁢      xe2x80x83    ⁢  α  ⁢      xe2x80x83    ⁢            ∑              ϵ        i              ⁢          δ      ⁡              (                  E          -                      ϵ            i                          )            
where xcex51 are discrete energy levels and xcex4 is the Dirac function. Thus, an enhanced density of states is a possibility even in partially confined QD superlattice (QDSL) structures.
It would, therefore, be desirable to provide a thermoelectric material or materials having a superlattice structure which have a relatively high thermoelectric figure of merit and which are suitable for usage in power generation systems, and in heating and/or cooling applications.
In view of the above, it has been recognized that an enhancement in the Seebeck coefficient, S, and the thermoelectric power factor, P=S2"sgr" may occur for a suitable quantum dot (QD) superlattice (SL) structure in which the chemical potential lies within a few kTs of the delta-like function of the ground state or one of the excited states of the partially confined QDs. In addition, the chemical potential should lie near a suitable band edge of a good thermoelectric material. In real materials, tunneling, thermal and inhomogeneous broadening as well as a weak potential barrier surrounding the QD may contribute to reducing the confinement effect. An enhancement of the Seebeck coefficient and the power factor in the PbSeTe/PbTe QDSL system have been found.
In addition to the possibility of an enhancement in the power factor, it has been recognized that another advantage of having a QDSL structure is the enormous density of dissimilar materials interfaces (involving the wetting layer, the matrix layer, and dot layer of the QDSL structure) which is expected to lower the lattice thermal conductivity to values below those attainable by merely alloying. Tests on the reduction of the thermal conductivity of superlattices have shown that the values were much lower than that of their constituents and even smaller than the thermal conductivity value of the equivalent compositional alloys. It is thus believed that phonon engineering combined with power-factor engineering may result in large improvements in the ZT of already good thermoelectric materials.
In accordance with the present invention, a quantum dot superlattice (QDSL) includes a first plurality of layers formed from PbSeTe at least one of which has a quantum dot formed thereon and a second plurality of layers formed from PbTe with the PbTe layers corresponding to re-planarization layers over the layers having the QDs formed thereon and having characteristics such that the QDSL is provided having a relatively high thermoelectric figure of merit.
Large increases in Seebeck coefficient (S), power factor and thermoelectric figure of merit (ZT) have been measured in PbSeTe/PbTe quantum dot superlattice structures (QDSLs). The improvement in ZT is attributed to the following: (1) a more favorable carrier scattering mechanism due to adsorbed or precipitated extra Te, (2) the presence of PbSe0.98Te0.02 islands imbedded in a PbTe matrix and believed to result in partial confinement of electrons in QDs, and (3) the lowering of the lattice thermal conductivity to at least the values of the homogeneous pseudobinary PbSexTe1xe2x88x92x alloys. Experimental values for the Pb-chalcogenide film in-plane room-temperature ZT values have been increased from approximately 0.52 for PbTe/Te structures to 0.88 for PbSe0.98Te0.02/PbTe QDSL structures. Further improvements in the ZT are anticipated based on the potential for lowering the lattice thermal conductivity because of the enormous number of dissimilar materials interfaces present in QDSL structures with periods in the 10-nm range. Also, many variables can be optimized including but not limited to the quantum dot quality, size, density, the substrate temperature, the growth rate, the stability of the beam equivalent fluxes with respect to time for thick films, post-growth procedures such as cool-down rate and annealing time and temperature. Optimization may also be possible by alloying with other compounds such as SmTe and PbS, for example. Of particular interest is the PbSmSSeTe/PbTe material system.
The thermoelectric properties of PbSexTe1xe2x88x92x/PbTe quantum-dot superlattices for possible improved thermoelectric materials have been investigated and found to provide enhancements in Seebeck coefficient and thermoelectric figure of merit (ZT) relative to bulk values. It is believed that such improvements are due to the various physics and, materials science phenomena associated with the quantum-dot structures have been found. ZT values approximately double the best bulk PbTe values, with ZT as high as about 0.9 at 300xc2x0 K. and conservatively estimated values as high as 2.0 at higher temperatures have been obtained in tests.
In accordance with the present invention, a QDSL structure includes a first plurality of layers of PbSeTe, each of said first plurality of layers including at least one quantum dot and a second plurality of layers of PbTe disposed in alternating relationship with the first plurality of layers of PbSeTe. With this particular arrangement, a superlattice structure is provided having a relatively high thermoelectric figure of merit (ZT). A superlattice having alternating layers of lead-selenide-telluride (PbSeTe) and lead-telluride (PbTe) is hereafter referred to as xe2x80x9cPbSeTe/PbTe SLxe2x80x9d). The PbSeTe layers of the PbSeTe/PbTe SL have a composition of PbSexTe1xe2x88x92x, where 0xe2x89xa6xe2x89xa61. In a preferred embodiment, x equals 0.98. It should be appreciated, however, that other values of x may result in QDSLs having equally high or even higher ZT values.
The PbSeTe/PbTe SL has a lattice thermal conductivity more than twice as low as typical lattice thermal conductivity values of PbTe. Moreover, the lattice layer combinations of the PbSeTe/PbTe SL give rise to a high power factor value. Additionally, the value of the Seebeck coefficient of the PbSeTe/ PbTe SL is also high because the SL has quantum dots and near optimal residual strain.
In contrast to the Pb1xe2x88x92xEux Te/PbSe quantum well superlattices, the PbSeTe quantum dot (QD) superlattice starts out growing each period as quantum wells on the PbTe matrix layer but after approximately two monolayers of PbSeTe growth, three-dimensional triangular-based pyramidal structures are formed. These nanometer-sized dots form because the strain in the lattice between the PbTe matrix material and the PbSeTe quantum-well material becomes too great for sustained atom-layer-by-atom-layer growth. In order to reduce the strain, the growth (Stranski-Krastanov growth mode) proceeds spontaneously as three-dimensional triangular-based PbSeTe pyramidal-shaped structures. There can be as many as 1011cmxe2x88x922 dots formed on the PbSeTe so-called wetting layer. The dot growth is halted at the optimal dot physical size and dot area density. Then, PbTe is grown to planarize the surface so that the growth mechanism reverts back to the atom-layer-by-atom-layer process. The above cycle has been repeated as many as 7,235 times or repetitions or periods, which results in sample thicknesses of up to approximately 100 micrometers.
For the Pb-chalcogenides, a lattice constant difference between the matrix and wetting layers of at least approximately 3% must occur in order for the strain to be large enough to cause the dots to form. For example, PbSe0.2Te0.8/PbTe superlattices do not form quantum dots because the lattice constant differential between PbSe0.2Te0.8 and PbTe is too small.
Tests on PbTe/PbSeTe superlattices show that these structures exhibit higher ZT values than the quantum well SL structures. It is believed that that the improved results are a consequence of the fact that the predominant mechanisms of the quantum well (QW) and QD structures are different. That is, even though the QW structures show enhanced ZT values due to electron confinement (as do the quantum dot structures), the enhancement effect is much stronger in the quantum dot structures. It has been learned that in order to achieve a ZT value of about 0.9 at room temperature, QDs were absolutely essential. That is, enhanced density of states due to the partial confinement of electrons in the quantum dot superlattice structure are believed to be essential to achieving the enhanced room temperature ZT values. In addition to the predominant carrier confinement mechanism due to QDs (and to a much lesser extent in the QWs), an optimal PbTe to Te flux ratio was needed in order to optimize the electron carrier scattering mechanism.